It is known, with cooled blades of gas turbines, to blow out cooling air at the blade tip, which for example promotes improved cooling of the seals which are arranged there. The cross sections of these outlet openings are generally dimensioned smaller than those of the cooling air passages. Therefore, they serve as restricting points and limit the mass flow of the cooling fluid which is blown out. The outlet openings customarily have circular or elliptical cross sections, and do not coincide with the cross-sectional shape of the cooling passage which guides the cooling air to the outlet opening. The abrupt cross-sectional change which consequently exists, results in unfavorable flow patterns which inter alia lead to increased pressure losses and locally increased material temperatures.